Museum of Natural History. admission by donation. so you can do just a few rooms and come back another day to do a few more. Worth 2 visits.
Metropolitan Museum of Art. admission by donation. There's armor and furniture and some nice art. Worth one visit.
Jewish children museum (listed above) good for a visit.
Brooklyn Children's Museum. has nice activities. Possibly worth a membership.-Which entitles you to entrance in various science museums.
Hall of Science in Queens. I haven't been there recently. It needs some parental interaction, but can be enjoyable. They used to close 2 pm -even on Sunday.
Liberty Science Center. I haven't been there since their big redo (5 or so years ago), so I don't know what's there now.
Other children's museums.
Get a new activity and /or game and have each kid invite a friend for a grand day of do and play.
Not in the winter:
Historic Hudson Valley. Especially the 'Sheep to Shawl' in Philipsburg Manor in the spring. Not cheap.
Bike riding. Either get a bike rack and bring your bikes or rent. Prosect Park. Sheepshead Bay. etc
Mini golf. Flushing Meadows Mini golf. check for coupons before you go.
Richmond Restoration, Staten Island